I have put a 100 gram weight ball in a plastic bottle and weight of this bottle is 20 gram .Now I shake this bottle in horizontal direction towards 5 centimeter back and forth with the applying force of 1 newton .So what will be the kinetic energy of this ball?
To calculate the kinetic energy of the ball, we need to use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
First, let's calculate the velocity of the ball. Since the bottle is being shaken horizontally, we can assume that the ball moves back and forth along a straight line. The distance traveled by the ball in one complete back and forth motion is twice the amplitude, which is 5 centimeters or 0.05 meters.
So, the total distance traveled by the ball in one complete back and forth motion is 2 * 0.05 = 0.1 meters.
Now, let's calculate the time it takes for one complete back and forth motion. Since you haven't mentioned the period or frequency, let's assume that the ball completes one full vibration cycle in 1 second.
The velocity of the ball can be calculated by dividing the distance traveled by the time taken:
Velocity = Distance / Time = 0.1 / 1 = 0.1 meters/second
Now, we have the mass of the ball as 100 grams or 0.1 kilograms and the velocity as 0.1 meters/second. Plugging these values into the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy = (1/2) * 0.1 * (0.1)^2
Kinetic Energy = (1/2) * 0.1 * 0.01
Kinetic Energy = 0.005 Joules or 5 millijoules
Therefore, the kinetic energy of the ball is 0.005 Joules or 5 millijoules.